Theme Essential Question: How are sampling of a populations used to make valid inferences and/or predictions about their respective general populations?
Essential Questions: How can you use measures of center and variability to compare two populations?
Standards
7. SP.3. Informally asses the degree of visual overlap of two numerical data distributions with similar variability, measuring the difference between the centers by expressing it as a multiple of a measure of variability.
7. SP.4. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.
Objectives:Review
The student will calculate the mean, median, mode and range.
The student will be able to find missing values in the data set for the mean.
The student will apply measure of central tendency to solve real-world problems.
The student will use measures of center and variability to compare two populations.
Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team (Taken from Ohio Dept of Education Mathematics Model Curriculum 6-28-2011 ) In Grade 6, students used measures of center and variability to describe sets of data. In the cluster “Use random sampling to draw inferences about a population” of Statistics and Probability in Grade 7, students learn to draw inferences about one population from a random sampling of that population. Students continue using these skills to draw informal comparative inferences about two populations.
Provide opportunities for students to deal with small populations, determining measures of center and variability for each population. Then have students compare those measures and make inferences. The use of graphical representations of the same data (Grade 6) provides another method for making comparisons. Students begin to develop understanding of the benefits of each method by analyzing data with both methods.
When students study large populations, random sampling is used as a basis for the population inference. This build on the skill developed in the Grade 7 cluster “Use random sampling to draw inferences about a population” of Statistics and Probability. Measures of center and variability are used to make inferences on each of the general populations. Then the students have make comparisons for the two populations based on those inferences.
This is a great opportunity to have students examine how different inferences can be made based on the same two sets of data. Have students investigate how advertising agencies uses data to persuade customers to use their products. Additionally, provide students with two populations and have them use the data to persuade both sides of an argument.
Recommended: For a quick overview of the standard(s) to be addressed in this Unit, see Arizona’s Content Standards Reference Materials at http://www.azed.gov/educator-certification/
This lesson has students explore and compare data sets and statistics in baseball. The lesson concludes with two part assessment section:
Student groups compare and evaluate each other’s solution. If they are different, they are to explain if it is a better answer or if it is merely a different form of the same answer.
Each student is to write a one paragraph response to the following problem: If a batter has a .400 batting average and gets a hit the first time at bat in a game, what are the odds of his getting a hit in his second at bat? His third? His fourth? Will this change depending on which part of the season it is?
or
Use the, Teaching the Common Core Math Standards with Hands-On Activities, as a reference to apply the learning to allow students to recreate the experience.
How Well Did They Do?, p. 133-135 Provide students with additional test score data to conduct a similar analysis.
What Can We Say?, p136 – 138 Allow students the opportunity to investigate other items.
or
Students can selection and collect data for a comparison based on their interest.
Key Questions
How do you informally assess the degree of visual overlap of two numerical data distributions with similar variabilities?
How do you use the measure of center and measure of variability for numerical data from a random sample to draw informative inferences about two populations?
. Observable Student Behaviors (Performance)
The student can compare two sets of data that have similar variabilities.
The student can make inferences about two populations using measures of center and variability.
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Vocabulary:
Math
Variability inference Mean absolute deviation
Suggested Activities:
Houghton Mifflin On Core Mathematics Middle School Grade 7
Unit 6-3, p. 145-138
Unit 6-4, p. 149-154 (Problem Solving Connections Unit 6)
ABC Mastering the Common Core in Mathematics
Review
Chapter 14.1, Range, p. 177
Chapter 14.2, Mean, p.178
Chapter 14.3, Finding data missing from the mean p.179
Chapter 14.4, Median, p. 180
Chapter 14.5, Mode, p 181
Chapter 14.6, Applying Measures of Central Tendency, p.182
Chapter 14.7, Comparing two sets of data, p 183
Chapter Review and test, p. 187
Gizmo Correlation
7.SP.4
Constructing Box-and-Whisker Plots
Construct a box and whisker plot to match a line plots, and construct a line plot to match a box and whisker plots. Manipulate the line plot and examine how the box and whisker plot changes. Then manipulate the box and whisker plot and examine how the line plot changes.
Sight vs. Sound Reactions
Measure your reaction time by clicking your mouse as quickly as possible when visual or auditory stimuli are presented. The individual response times are recorded, as well as the mean and standard deviation for each test. A histogram of data shows overall trends in sight and sound response times. The type of test as well as the symbols and sounds used are chosen by the user. (Student Exploration Sheet & Teacher Guide Available)
Highly Recommended: None available at this time
JBM 8th GP 3, p 277-334
Teaching the Common Core Math Standards with Hands-On Activities,
Mathematics in Children's Literature: Many children's books include math concepts and can be used to help teach them in a fun way. This website includes several annotated Lists of Children's Literature including the math concepts and grade levels.
The teaching Channel currently offers videos of K-12 mathematics teaching aligned with the Common Core Sate Standards, which would be perfect for professional development with teacher teams.
Interactivate is a set of free, online courseware for exploration in science and mathematics. It is comprised of activities, lessons, and discussions. The site is structured around collections of activities, lessons, and discussions.
Thinkfinity Links: Search by Common Core Standards/Seventh Grade/Math Often students are confused about ‘where to start’ when solving a multi-step equation. In this lesson the equation is labeled as a ‘party’. The 'host' is labeled (x) with remaining operations being labeled according to their relationship to the host (friends, family, acquaintances, etc...). Technology assignments are used as one method to assess student understanding.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Grade: 7 Unit: 5 Week: 4
Content: Comparing Populations
Problem Solving Connections
Dates: 4/1/2013 – 4/5/2013
Theme Essential Question:
How are sampling of a populations used to make valid inferences and/or predictions about their respective general populations?
Essential Questions:
How can you use measures of center and variability to compare two populations?
Standards
Objectives:Review
Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team
(Taken from Ohio Dept of Education Mathematics Model Curriculum 6-28-2011 )
In Grade 6, students used measures of center and variability to describe sets of data. In the cluster “Use random sampling to draw inferences about a population” of Statistics and Probability in Grade 7, students learn to draw inferences about one population from a random sampling of that population. Students continue using these skills to draw informal comparative inferences about two populations.
Provide opportunities for students to deal with small populations, determining measures of center and variability for each population. Then have students compare those measures and make inferences. The use of graphical representations of the same data (Grade 6) provides another method for making comparisons. Students begin to develop understanding of the benefits of each method by analyzing data with both methods.
When students study large populations, random sampling is used as a basis for the population inference. This build on the skill developed in the Grade 7 cluster “Use random sampling to draw inferences about a population” of Statistics and Probability. Measures of center and variability are used to make inferences on each of the general populations. Then the students have make comparisons for the two populations based on those inferences.
This is a great opportunity to have students examine how different inferences can be made based on the same two sets of data. Have students investigate how advertising agencies uses data to persuade customers to use their products. Additionally, provide students with two populations and have them use the data to persuade both sides of an argument.
Recommended: For a quick overview of the standard(s) to be addressed in this Unit, see Arizona’s Content Standards Reference Materials at http://www.azed.gov/educator-certification/
Assessment:
Product:
This lesson has students explore and compare data sets and statistics in baseball. The lesson concludes with two part assessment section:
- Student groups compare and evaluate each other’s solution. If they are different, they are to explain if it is a better answer or if it is merely a different form of the same answer.
- Each student is to write a one paragraph response to the following problem: If a batter has a .400 batting average and gets a hit the first time at bat in a game, what are the odds of his getting a hit in his second at bat? His third? His fourth? Will this change depending on which part of the season it is?
or- Use the, Teaching the Common Core Math Standards with Hands-On Activities, as a reference to apply the learning to allow students to recreate the experience.
- How Well Did They Do?, p. 133-135 Provide students with additional test score data to conduct a similar analysis.
- What Can We Say?, p136 – 138 Allow students the opportunity to investigate other items.
orKey Questions
- How do you informally assess the degree of visual overlap of two numerical data distributions with similar variabilities?
- How do you use the measure of center and measure of variability for numerical data from a random sample to draw informative inferences about two populations?
.Observable Student Behaviors (Performance)
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Vocabulary:
Suggested Activities:
- Houghton Mifflin On Core Mathematics Middle School Grade 7
- Unit 6-3, p. 145-138
- Unit 6-4, p. 149-154 (Problem Solving Connections Unit 6)
- ABC Mastering the Common Core in Mathematics
- Review
- Chapter 14.1, Range, p. 177
- Chapter 14.2, Mean, p.178
- Chapter 14.3, Finding data missing from the mean p.179
- Chapter 14.4, Median, p. 180
- Chapter 14.5, Mode, p 181
- Chapter 14.6, Applying Measures of Central Tendency, p.182
- Chapter 14.7, Comparing two sets of data, p 183
- Chapter Review and test, p. 187
Gizmo Correlation- 7.SP.4
- Constructing Box-and-Whisker Plots
- Construct a box and whisker plot to match a line plots, and construct a line plot to match a box and whisker plots. Manipulate the line plot and examine how the box and whisker plot changes. Then manipulate the box and whisker plot and examine how the line plot changes.
- Sight vs. Sound Reactions
- Measure your reaction time by clicking your mouse as quickly as possible when visual or auditory stimuli are presented. The individual response times are recorded, as well as the mean and standard deviation for each test. A histogram of data shows overall trends in sight and sound response times. The type of test as well as the symbols and sounds used are chosen by the user. (Student Exploration Sheet & Teacher Guide Available)
Highly Recommended: None available at this timeDiverse Learners
Homework: (Teacher Discretion)
Terminology for Teachers:
Mean absolute deviation (MAD) is a new term that teachers need to study and be familiar with before this lesson begins.
Ethnicity/Culture | Immigration/Migration | Intercultural Competence | Socialization | Racism/Discrimination
High Yield Strategies
Similarities/Differences | Summarizing/Notetaking | Reinforcing/Recognition | Homework/Practice |
Non-Linguistic representation | Cooperative Learning | Objectives/Feedback |
Generating-Testing Hypothesis | Cues, Questions, Organizers
Resources:
Professional Texts:
Literary Texts
- Mathematics in Children's Literature: Many children's books include math concepts and can be used to help teach them in a fun way. This website includes several annotated Lists of Children's Literature including the math concepts and grade levels.
Click on the following link, http://libguides.nl.edu/mathinchildrenslit, and then look under Math and Literature Bibliographies.- Middle & High School: Literature in Mathematics
Many books include websites with lesson ideas.http://sci.tamucc.edu/~eyoung/middle_school_literature.html
- Lesson Plans for Using Literature in Middle and High School Mathematics (developed by Leonor and edited by Elaine)
http://sci.tamucc.edu/~eyoung/Literature%20webpages/Leonor/index.html- Miscellaneous Math and Children's Literature
http://sci.tamucc.edu/~eyoung/literature.htmlInformational Texts
Art, Music, and Media
Manipulatives
Games
Videos
SMART Board Lesson, Promethean Lessons
Other Activities, etc.
- http://www.mathgoodies.com/lessons/vol5/division.html
- http://www.math.com/school/subject1/lessons/S1U1L12GL.html
- Interactivate is a set of free, online courseware for exploration in science and mathematics. It is comprised of activities, lessons, and discussions. The site is structured around collections of activities, lessons, and discussions.
http://www.shodor.org/interactivate/guide/Activities and tools:
http://www.shodor.org/interactivate/activities/
- Thinkfinity Links: Search by Common Core Standards/Seventh Grade/Math Often students are confused about ‘where to start’ when solving a multi-step equation. In this lesson the equation is labeled as a ‘party’. The 'host' is labeled (x) with remaining operations being labeled according to their relationship to the host (friends, family, acquaintances, etc...). Technology assignments are used as one method to assess student understanding.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
- Thinkfinity Links: Search by Common Core Standards/Seventh Grade/Math http://www.thinkfinity.org/state-standards-search
- Website tool: http://curvebank.calstatela.edu/circle/circle.htm
- The Area of a Circle-The method of rearranging http://www.themathpage.com/aTrig/area.htm
- Website tools:
http://www.ixl.com/math/grade-5/radius-diameter-circumference-and-area-of-a-circlehttp://curvebank.calstatela.edu/circle/circle.htm
Language
Arts
Week 1
Week 2
Week 3
Week 4
7 Matrix
Accelerated 7
Matrix
Week 1
Week 2
Week 3
Week 4
Home K-2
Home 3-6
Home 6-8
Unit 1
Unit 2
Unit 3
Unit 4